- Warren Koepp
Changing the value of "a" with the slider changes the base on the blue curve, which is y=c*a^(x-h) + k. The red curve is y=c*(1/a)^(x-h) + k, i.e. its base is the reciprocal of the base for the blue exponential function. The parameter "c" stretches/compresses the graphs vertically, while "h" slides the graph left/right and "k" moves them up and down. The beginning values of c, h, and k are set so that there is no stretching or sliding of graphs. The dotted green line (which is along the y=axis initially) is the line y=k, which is the horizontal asymptote of the graphs.
Use the slider to change the base--it goes from 0.1 up to 10, in increments of 0.1. What happens when a=1? How do the graphs' positions change when the based is changed from 2 to 0.5? Why? What happens as you increase c? What if c is negative? Can you move the curves up 3 units? Left 2 units?